JournalsjstVol. 3, No. 1pp. 101–128

Spectral analysis of tridiagonal Fibonacci Hamiltonians

  • William Yessen

    Rice University, Houston, USA
Spectral analysis of tridiagonal Fibonacci Hamiltonians cover
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Abstract

We consider a family of discrete Jacobi operators on the one-dimensional integer lattice, with the diagonal and the off-diagonal entries given by two sequences generated by the Fibonacci substitution on two letters. We show that the spectrum is a Cantor set of zero Lebesgue measure, and discuss its fractal structure and Hausdorff dimension. We also extend some known results on the diagonal and the off-diagonal Fibonacci Hamiltonians.

Cite this article

William Yessen, Spectral analysis of tridiagonal Fibonacci Hamiltonians. J. Spectr. Theory 3 (2013), no. 1, pp. 101–128

DOI 10.4171/JST/39